SPRING FORCE PHYSICS (HOOKE's LAW and APPLICATIONS) PHYSICS EXPECTATIONS: SPH4U: B2.3, B2.4, B2.5, C3.1 VIDEO: Youtu.Be/Sf6xpywoixa

SCIENCE AT HOME GRADE: 12 SPH4U SUBJECT: PHYSICS STRAND: DYNAMICS, ENERGY AND SPRING FORCE MOMENTUM TOPIC: SPRING FORCE PHYSICS (HOOKE'S LAW AND APPLICATIONS) PHYSICS EXPECTATIONS: SPH4U: B2.3, B2.4, B2.5, C3.1 VIDEO: youtu.be/SF6XpyWoixA

INTRODUCTION: A force is a push or pull that, if acting alone, will cause a change to the way an object is moving.

Gravity, a pulling force, is often the first one that we learn about. Earth’s gravity pulls objects toward the Earth’s centre. We calculate the force of gravity "near Earth," or "Fg," as Fg = mg, where m is an object’s mass, In this activity, you will be creating a model for and g is the constant acceleration due to how a certain force — the spring force gravity experienced by objects "near" the —behaves, and see how it relates to the normal surface of the Earth. Because the force of force. gravity near Earth depends only on the object’s mass and not on its position, we say ACTIVITY: Investigate spring force that it’s a constant force. Moving an object up or down, left or right, won’t change the TIME: 30 minutes gravitational force acting on it. SAFETY: The "normal force" is a push that prevents objects from moving through one another. Wear glasses, sunglasses or safety goggles to When you set a book on a table, gravity pulls protect your eyes in case an elastic breaks. the book downwards, but the normal force from the table pushes it back up. If these WHAT YOU NEED: forces — gravity and the normal force — are in balance, the book won’t move. • Ruler

Gravity is a constant and fundamental force, • Elastic band, hair tie, spring (the easier to but what about the normal force? Are all stretch, the better) forces constant, or do they depend on • Banana holder or another stand that an position? And what is the normal force really? elastic can be hung from

To answer these kinds of questions, physicists • Container (an envelope, for instance) to hold build simple models. They use their models to mass make predictions and then test those predictions with experiments. Models are constantly tested. When a model fails to make a prediction, it needs to be improved, or replaced altogether.

An agency of the Government of Ontario SCIENCE AT HOME GRADE: 12 SPH4U SUBJECT: PHYSICS STRAND: DYNAMICS, ENERGY AND SPRING FORCE MOMENTUM TOPIC: SPRING FORCE PHYSICS (HOOKE'S LAW AND APPLICATIONS) PHYSICS EXPECTATIONS: SPH4U: B2.3, B2.4, B2.5, C3.1 VIDEO: youtu.be/SF6XpyWoixA

WHAT YOU NEED (continued): • Nickels or other objects with masses • Keep adding weights. Measure the length of identical to each other (like coins or the elastic each time. If you're okay with marbles) breaking your elastic, keep adding weights, and record the point when it breaks. • Tape • Graph your results with the length of the • Paper elastic on the x-axis and the elastic force on the y-axis. • Pencil Hint: To determine the elastic force, draw a • Calculator free-body diagram, showing the magnitude and direction of all the forces acting on the WHAT YOU DO: container.

• Attach an elastic to the banana holder or • Looking at your graph, try to come up with a stand. simple equation for the elastic or spring • To the other end of the elastic band, attach force as a function of the elastic’s length. the container, so that it hangs down. What kind of function does it look like?

• Use a ruler to measure the starting length of • Using your graph, try to come up with a the elastic. simple equation for spring force. When does the equation hold and when does it break? • Add a weight to the container and observe How does your equation for spring force what happens to the elastic and the compare to the equations for other forces container. Record the length of the elastic. you’ve learned about — for instance, gravity? Banana stand

Rubber band Tracking sheet

Container for masses

Ruler

WHY THIS MATTERS: It turns out that spring force is not a constant Note: In this activity, you will be bending or force — it depends on the amount that an stretching objects, possibly to their breaking object stretches or compresses. This point. Make sure you select a couple of relationship is described by Hooke’s Law: Fs = kx. objects that you are okay with breaking (for

The spring force (Fs) is equal to the distance instance, sticks from outside). stretched or compressed (x) multiplied by a spring constant (k). It’s important to remember WHAT YOU DO: that physicists don’t come up with these equations off the top of their heads; it was • All objects, even ones we think of as rigid, hypothesized, tested and refined through exhibit spring properties when you stretch or experiments like the one you just did. compress them before they eventually break. As you continue in your studies, you will learn • Select an object and apply a gentle force to that other important forces, like universal it and then release. Watch how the object gravitation and the electrostatic force, are not bends and then returns to its original shape, constant. just like an elastic.

ACTIVITY: Investigate how all • Apply more and more force to the object. materials behave like elastics Does it still snap back to its original shape and springs when you let go? TIME: 15 minutes • Apply enough force so that the object does not snap back to its original shape. (Make SAFETY: sure you're using objects that you don't mind breaking). When does it reach a Wear glasses, sunglasses or safety goggles to breaking point? Where does it break? protect your eyes in case something breaks. • Repeat the experiment using other WHAT YOU NEED: materials. Which ones can handle the most force before they deform or break? Which • Foam blocks ones can bend or compress the furthest and still return to their original shape? • Paper towel rolls

• Wooden, plastic or metal board

• Any long cylinder or rectangular prism (for instance, sticks, kitchen utensils, pencils, etc.)

• Water

WHY THIS MATTERS: Every object, even rigid things like tables and floors, behaves like a spring if you look closely enough. When you stand on a floor, it bends or compresses like a spring and exerts a force back on you. We usually call this the "normal force," but as you can see, the normal force is not a fundamental one. In this case, the normal force is really a spring force caused by the compression of the floor.

Eventually, objects will reach a breaking point where they stop acting like springs. Materials scientists study materials to determine their spring constants and the maximum forces they can withstand before they deform or break.

Once you’ve determined this maximum force, you can use that information (along with "inelastic collisions" and "conservation of energy") to figure out, for instance, how fast you need to swing your arm to break boards the way martial artists do!

MORE ONLINE: How to determine the spring constant https://www.youtube.com/watch?v=tdy _wHZfdTo

Normal Force Demo https://www.youtube.com/watch?v=7l4iFXN0 at0&feature=youtu.be

Hooke’s Law and Young’s Modulus https://www.youtube.com/watch?v=qvcpeA5 pBH0&feature=youtu.be

An agency of the Government of Ontario